HYDROSTATIC

HYDROSTATIC

• branch of fluid mechanics that studies fluids at rest. It embraces the study of the conditions under which fluids are at rest in stable equilibrium; and is contrasted with fluid dynamics, the study of fluids in motion.

• The fundamental of Hydraulic

• Hydrostatics offers physical explanations for many phenomena of everyday life, such as why atmospheric pressure changes with altitude, why wood and oil float on water, and why the surface of water is always flat and horizontal whatever the shape of its container.

HYDROSTATIC PRESSURE• HYDROSTATIC PRESSURE is the pressure present within a fluid when it is at rest

• It acts equally in all Direction

• It acts a right angle to any surface in contact with the liquid

Pressure

Hydraulics

• dealing with the mechanical properties of liquid

• Liquid version pf pneumatic

Free surface hydraulics• the branch of hydraulics dealing with free

surface flow, such as occurring in rivers, canals, lakes, estuariesand seas. Its sub-field open channel flow studies the flow in open channels.

Hydrostatic Pressure

• Hydrostatic pressure is the weight per unit area

• ph = g A D / A

ph = g D

Holds for = constant

Often ph = - g z (z+ up)

D

ph = g D

• Let, D = 100 m & = 1025 kg m-3

• Hydrostatic Pressure, ph = g D

= (1025 kg m-3) (9.8 m s-2) (100 m)

= 1,004,500 kg m-1 s-2 [=N/m2]

Hydrostatic Pressure Example

• ph = 1,004,500 N m-2

• 1 N m-2 = 1 Pascal pressure

• 105 Pa = 1 bar = 10 db

• ph = 1,004,500 Pa (10 db/105 Pa)

= 100.45 db

Example Cont. (or unit hell)

• First, 100 m depth gave a ph =

100.45 db

• Rule of thumb:

1 db pressure ~ 1 m depth

1 db ~ 1m

• Total pressure = hydrostatic + atmospheric

pt = ph + pa

• pa varies from 950 to 1050 mb (9.5-10.5 db)

• pa = ph(@~10 m)

• Mass atmosphere = mass top 10 m ocean

Total Pressure

Dealing with Stratification

• Density is a f(depth)

• Taking a layer approach

dp = (z) g dz

dz = layer thickness [m]

• Summing over D

ph = (z) g dz (where over depth, D)

D

Example with Stratification

24.5 25 25.5 26 26.5-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0Sigma - t

(kg m-3)

dept

h (m

)

1 = 1025 kg m-3

2 = increases from 1025 to 1026 kg m-3

What is ph(100m)??

Example with Stratification

• Sum over the top 2 layers

ph(100 m) = ph(layer 1) + ph(layer 2)

• Layer 1:

ph(1) = (1025 kg m-3) (9.8 m s-2) (50 m)

= 502,250 N m-2 (or Pa)

105 Pa = 10 db

ph(1) = 50.22 db

Example with Stratification

• Layer 2:

Trick: Use average density!!

ph(2) = (1025.5 kg m-3) (9.8 m s-2) (50 m)

= 502,500 Pa = 50.25 db

• Sum over top 2 layers

ph(100 m) = ph(1) + ph(2)

= 50.22 + 50.25 = 100.47 db

Hydrostatic Pressure

• Hydrostatic relationship: ph = g D

• Links water properties () to pressure

• Given (z), we can calculate ph

• Proved that 1 db ~ 1 m depth

• Showed the atmospheric pressure is small part of the total seen at depth